图是λ_4-最优的和超级-λ_4的充分条件

Sufficient conditions of a λ_4-optimal and super-λ_4 graph

设G是有限简单无向图,是G-U不连通,且G-U的每个分支的阶都至少为4的边集U称为G的4-限制边割。基数最小的4-限制边割称为λ4-割,最小基数称作4-限制边连通度,记作λ4=λ4(G)。若λ4(G)=ξ4(G),称G是λ4-最优的。若任意一个λ4-割都孤立一个四阶连通子图,则称G是超级-λ4的。应用邻域交条件给出了图是λ4-最优的和超级-λ4的充分条件。

Let G be a finite, simple and undirected graph and U be its edge subset If G-U is disconnected and each component of G-U contains at least four vertices, then such an edge set is 4-restricted edge-cut of G. The 4-restricted edge-cut U whose cardinality is the smallest is called a λ4- cut, and its cardinality is called the 4-restricted edge-connectivity, denoted by λ4 = λ4（G） , G is λ4-optimal if λ4 = so4 （G） and super-λ4 if every A4-cut isolates a connected subgraph of order 4. This paper presents some sufficient conditions for a λ4-optimal and super-λ4 graph with the neighborhood intersection condition.